What are some of your favorite basic math hacks?(borovik.net)

3 pointsby ColinWrightil y a 5 ans6 comments

What are some of your favorite basic math hacks?

https://www.borovik.net/selecta/uncategorized/what-are-some-of-your-favorite-basic-math-hacks/

6 comments

"The essence of mathematics is in universal methods for solving all problems in a particular class of problems. Use of “hacks”/”tricks” is a replacement of mathematics by cheap surrogates. Hacks/tricks can work at a certain level, but frequently obstruct students’ progress at the next level of learning of mathematics."

I would have to agree with the article.

I tried to learn the Trachtenberg system [1] a while back. I thought it would be a simple and fun thing to do. Maybe it's just my brain but I couldn't wrap my head around all the different rules for simple multiplication. Rather than speeding up my mental arithmatic it slowed it down considerably. In the end I gave up, feeling a little bit more stupid than when I started.

[1] https://en.wikipedia.org/wiki/Trachtenberg_system

sunnyamil y a 5 ans

What are you classifying as a hack? I've always enjoyed the trick for squaring numbers ending in 5. You take the number(s) before the last 5 and multiply it with the number above and add 25 to the end,

So for 4545, you do 45, which is 20 and add 25 to the end, giving 2025.

That's a fun one because it's quicker to do it in your head than it is to type it into a calculator.

jonsenil y a 5 ans

The trick can make any square easier. Take 27 * 27, make it 3 up and 3 down, i.e. 30 * 24 = 720. Then adding the 3 squared you get the answer 729.

ColinWrightil y a 5 ans

You need to deal with the formatting issues in your reply ... the "" creates italics unless treated carefully.

So you mean:

"So for 45x45, you do 4x5, which is 20 and add 25 to the end, giving 2025."*

And while that's interesting, it does feel like you're simply responding to the question/title, rather than reading and responding to the actual article.

sunnyamil y a 5 ans

Thanks! Yes, formatting messaged up.

I did read your article but I felt that it buckets all hacks together as an unnecessary evil in education.

I think it's quite a nice confidence booster to know a method that would speed them up (usually in basic arithmetic). It also provides a future learning opportunity when trying to derive why a hack works.

I agree with the article, but I would really be interested in some in-depth examples of what the alternative to tricks/hacks are? I don't ever remember a case where I was only taught the hack, for example. We learn it the long way and then the teacher/lecturer might show us a quick version in passing. Is this not the case all of the time?

ColinWrightil y a 5 ans

> Thanks!

You're welcome.

> Yes, formatting messaged up.

Do you mean "messed up"? I can't make sense of "messaged up" but I'm guessing it doesn't matter.

> I did read your article ...

I didn't write it, so it's not really "my" article.

> ... I felt that it buckets all hacks together as an unnecessary evil in education.

I think in this case and this context, "hack" refers to "doing something a quick and dirty way without necessarily knowing how or why it works."

> I don't ever remember a case where I was only taught the hack, for example. We learn it the long way and then the teacher/lecturer might show us a quick version in passing. Is this not the case all of the time?

Then you are lucky, and no, it's not the case all the time. There are many cases of students being taught "Tricks" to get a result without them having any real understanding of what's going on. You don't need to spend very long talking to students about how they're solving exam problems to realise that in many (but not all!) cases they're just applying hacks, tricks, and processes without knowing why they work.